Measure 8 litres with a 10 and a 6

Question

You have a 10-litre jug and a 6-litre jug, neither with any markings, plus a tap and a drain. Moves are: fill a jug, empty a jug, or pour from one to the other until one is empty or the other is full. Get exactly 8 litres into the 10-litre jug. How few moves can it take? Note that 8 is not a multiple of 6 and not a difference you can make in one pour, so it needs a little planning.

Accepted Answer

Six moves. State written as (10-jug, 6-jug). 1. Fill the 10: (10, 0) 2. Pour into the 6 until full; 4 litres remain: (4, 6) 3. Empty the 6: (4, 0) 4. Pour the 4 across into the 6: (0, 4) 5. Fill the 10: (10, 4) 6. Pour into the 6; only 2 litres fit, leaving 8 in the 10-litre jug: (8, 6) Why this is the natural route. The first pour manufactures 4 litres, which is 10 minus 6. Parking those 4 litres in the small jug leaves only 2 litres of space there, so the next pour from a full big jug removes exactly 2, and 10 minus 2 = 8. In general, any amount you can write as a combination of the two jug…

Measure 8 litres with a 10 and a 6

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